Fluid interfaces with very sharp tips in viscous flow

Sylvain Courrech du Pont, Jens G Eggers

Research output: Contribution to journalArticle (Academic Journal)

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Abstract

When a fluid interface is subjected to a strong viscous flow,
it tends to develop near-conical ends with pointed tips so sharp,
their radius of curvature is undetectable. In microfluidic applications,
tips can be made to eject fine jets, from which micron-sized drops can
be produced. Here we show theoretically that the opening angle of the
conical interface varies on a logarithmic scale as function of the
distance from the tip, owing to
non-local coupling between the tip and the external flow. Using this
insight we are able to show that the tip curvature grows like the
exponential of the square of the strength of the external flow,
and to calculate the universal shape of the interface near the tip.
Our experiments confirm the scaling of the tip curvature as well as of the
interface's universal shape. Our analytical technique, based on an
integral over the surface, may also have far wider applications, for
example treating problems with electric fields, such as electrosprays.
Original languageEnglish
JournalProceedings of the National Academy of Sciences of the United States of America
Publication statusUnpublished - 2020

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